Advertisement

Calculation of Average Network Parameters Using Combined Kinetic and Markovian Analysis

  • Douglas R. Miller
  • Christopher W. Macosko

Abstract

Molecular and network parameters of branched polymer systems can he computed using various theoretical models and analysis techniques. Kinetic analysis and Markov modeling are two general approaches. For certain complex polymer systems the best approach may be a hybrid approach which combines kinetic and Markovian analysis. This hybrid approach is described in general, and several specific examples and applications are given.

Keywords

Substitution Effect Anionic Polymerization Intramolecular Bond Initial Species Markovian Analysis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Dusek, K., Formation structure relationship in polymer networks, Brit. Polym. J., 1985, 17, 185–89.CrossRefGoogle Scholar
  2. 2.
    Ziff, R. M., Kinetics of polymerization, J. Stat. Phys., 1980, 23, 241–63.CrossRefGoogle Scholar
  3. 3.
    Ziff, R. M. and Stell, G., Kinetics of polymer gelation, J. Chem. Phys., 1980, 73. 3492–9.CrossRefGoogle Scholar
  4. 4.
    Flory, P. J., Principles of Polymer Chemistry, Cornell University Press, Ithaca. New York, 1953.Google Scholar
  5. 5.
    Gordon, M., Good’s theory of cascade processes applied to the statistics of polymer distributions, Proc. Roy. Soc. London, 1962, A268, 240–59.Google Scholar
  6. 6.
    Macosko, C. W. and Miller, D. R., A new derivation of average molecular weights of nonlinear polymers, Macromolecules, 1976, 9, 199–206.CrossRefGoogle Scholar
  7. 7.
    Burchard, W., Static and dynamic light scattering from branched polymers and biopolymers, Adv. Polym Sci., 1983, 48, 1–124.CrossRefGoogle Scholar
  8. 8.
    Dusek, K., Network formation in curing of epoxy resins, Adv. Polym. Sci., 1986. 78, 1–58.CrossRefGoogle Scholar
  9. 9.
    Miller, D. R. and Macosko, C. W., Substitution effects in property relations for stepwise polyfunctional polymerization, Macromolecules, 1980, 13, 1063–89.CrossRefGoogle Scholar
  10. 10.
    Miller, D. R. and Macosko, C. W., Molecular weight relations for crosslinking of chains with length and site distribution, J. Polym. Sci., Phys. Ed., 1987, 25, 2441–69.CrossRefGoogle Scholar
  11. 11.
    Miller, D. R. and Macosko, C. W., Network parameters for crosslinking of chains with length and site distribution, J. Polym. Sci., Phys. Ed., 1988, 26, 1–54.CrossRefGoogle Scholar
  12. 12.
    Sarmoria, C., Valles, E. M. and Miller, D. R., Ring-chain competition kinetic models for linear and nonlinear step-reaction copolymerizations, Maeromol. Chem., Maeromol. Symp., 1986, 2, 69–87.CrossRefGoogle Scholar
  13. 13.
    Sarmoria, C., Valles, E. M. and Miller, D. R., Models for nonlinear step-reaction polymerisations with intramolecular reactions, 1988, in press.Google Scholar
  14. 14.
    Gordon, M. and Scantlebury, G. R., Theory of ring-chain equilibria in branched non-random polycondensation system, with applications to POCl3/P2O5, Proc. Roy. Soc. London, 1966, A292, 380.Google Scholar
  15. 15.
    Bokare, U. M. and Gandhi, K. S., Effect of simultaneous polyaddition reaction on the curing of epoxides, J. Polym. Sci., Chem. Ed., 1980, 18, 857–70.CrossRefGoogle Scholar
  16. 16.
    Dusek, K., Build-up of polymer networks by initiated polyreactions 2. Theoretical treatment of polyetherification released by polyamine polyepoxide addition, Polym. Bull., 1985, 13, 321–8.CrossRefGoogle Scholar
  17. 17.
    Riccardi, C. C. and Williams, R. J. J., Statistical structural model for the buildup of epoxy-amine networks with simultaneous etherification, Polymer, 1986, 27, 913–20.CrossRefGoogle Scholar
  18. 18.
    Riccardi, C. C. and Williams, R. J. J., Kinetic and statistics of the formation of epoxy-amine networks with simultaneous etherilication, 1987, in press.Google Scholar
  19. 19.
    Worsfold, D. J., Anionic copolymerization of styrene and p-divinylbenzene, Macromolecules, 1970, 3, 514–17.CrossRefGoogle Scholar
  20. 20.
    Lutz, P., Beinert, G. and Rempp, P., Anionic polymerization and copolymerization of 1,3- and 1,4-diisopropenylbenzene, Makromol. Chem., 1982, 183, 2787–97.CrossRefGoogle Scholar
  21. 21.
    Dusek, K. and Somvârsky, J., Build-up of polymer networks by initiated polyreactions 1. Comparison of kinetic and statistical approaches to the living polymerization type of build-up, Polym. Bull., 1985, 13, 313–19.CrossRefGoogle Scholar

Copyright information

© Elsevier Applied Science Publishers Ltd 1988

Authors and Affiliations

  • Douglas R. Miller
    • 1
  • Christopher W. Macosko
    • 2
  1. 1.Department of Operations ResearchGeorge Washington UniversityUSA
  2. 2.Department of Chemical Engineering and Materials ScienceUniversity of MinnesotaMinneapolisUSA

Personalised recommendations